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  • Negative Cronbach's Alpha

    From Zhen Gie@21:1/5 to All on Mon Jun 19 02:56:50 2023
    Hi everyone,

    Recently I did a pilot study on adapting (14 items) a published scale (23 items). I stumped into a negative alpha value of -0.77 and item deletion wouldn't make it any better either. Where and how do I proceed from this?

    Link to the excel and output if anyone could help with this: https://drive.google.com/drive/folders/1KKz1pTZLka9g4XPtZ9E9PkKc5cG1JMLc?usp=sharing

    -Zhen

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  • From Rich Ulrich@21:1/5 to [email protected] on Mon Jun 19 19:37:09 2023
    On Mon, 19 Jun 2023 02:56:50 -0700 (PDT), Zhen Gie
    <[email protected]> wrote:

    Hi everyone,

    Recently I did a pilot study on adapting (14 items) a published scale (23 items). I stumped into a negative alpha value of -0.77 and item deletion wouldn't make it any better either. Where and how do I proceed from this?

    Link to the excel and output if anyone could help with this: >https://drive.google.com/drive/folders/1KKz1pTZLka9g4XPtZ9E9PkKc5cG1JMLc?usp=sharing

    -Zhen

    I didn't know I could read that, but Firefox called up Google-docs
    or some-such, and it worked.

    I see the message at the bottom -
    a. The value is negative due to a negative average covariance among
    items. This violates reliability model assumptions. You may want to
    check item codings.

    I note:
    Assumption 1, all items are "scored in the same direction" so that
    an average correlation makes sense.
    Assumption 2, all variances are approximately equal, so that
    the items are weighted equally in the computation.

    I copied from an answer I gave in 2021:
    * *
    Where do negative alphas come from? -- SPSS Reliability does
    not know about "reversed scored" items; you need to be sure
    that all variables which you pass to the Reliability program
    are scored so that low numbers always represent "low" on
    whatever you label the scale. (To fix: Scores may be "reflected"
    by subtraction -- X in the range of 1-4 becomes X_rev in the
    range of 4-1 after you subtract from 5). The resulting matrix
    of correlations will be (almost entirely) positive values.
    * *

    (There will be positive r's, if you have a sensible 'scale'.)

    Alpha is sort-of the average correlation, 'sort-of' because it is
    computed from covariances while assuming COV's are of similar
    magnitude. Your data has a wide range for variances, so implicit
    weightings are not equal. /Apparently/ the negative covariances
    are much larger than the positive.

    I notice that your total sample N is 12, one less than the number
    of items. That is why the squared multiple correlation is missing.

    That "Cronbach's alpha if item is deleted" which is reported as -1.043 surprises me - as being, possibly, an impossible value for an alpha.
    I'm not checking on the formulas, but I figure that the "if deleted" computation is an approximation, and it could be screwed up by
    your combination of small N and +/- covariances, with unequal
    variances implicitly being weighted very differently when 'adjusted'
    (while the computation assumes that variances are equal).

    Unequal variances: From the statistics, I gather that your items
    are scored from 0-3; the reduced SD is reported when the mean
    0.50 and lower and for mean=2.92. I suggest that your more
    robust estimate of alpha will be obtained by dropping those 5
    variables. Or, add them together to get one score, after doing
    the necessary reverse scoring.

    It is also nice to have an N of 30 or more when looking at
    individual correlations; but we work with what we have.

    --
    Rich Ulrich

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  • From Rich Ulrich@21:1/5 to [email protected] on Mon Jun 19 20:29:28 2023
    On Mon, 19 Jun 2023 19:37:09 -0400, Rich Ulrich
    <[email protected]> wrote:

    I copied from an answer I gave in 2021:
    * *
    Where do negative alphas come from? -- SPSS Reliability does
    not know about "reversed scored" items; you need to be sure
    that all variables which you pass to the Reliability program
    are scored so that low numbers always represent "low" on
    whatever you label the scale. (To fix: Scores may be "reflected"
    by subtraction -- X in the range of 1-4 becomes X_rev in the
    range of 4-1 after you subtract from 5). The resulting matrix
    of correlations will be (almost entirely) positive values.
    * *

    Maybe it is obvious which direction is "low" and maybe it
    is not. If not, how should you proceed?

    Even though the sample is tiny for a factor analysis, a FA should
    run and produce at least one principle component. If it won't run
    with the 13, drop the 5 items with low variance.

    Assuming that these items to represent some 'universe' of
    scores, all the items will load on the PC. About half the items
    will have positive loadings, and half will have negative.
    Consider that to be two sets; reverse-score one of the sets.

    (Which set the program computes as negative is a accident of
    the data and the implementation. I /think/ SPSS automatically
    reverses all the signs displayed for a factor when a majority of items
    were computed as negative. But I'm not sure of that.)

    It doesn't matter which set gets reversed, except the 'high' end
    probably illustrates what name you should give to the 'factor',
    considering especially the highest few loadings.

    --
    Rich Ulrich

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